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To construct a Markov chain, all we need
to know are the probability for each state (*M*-1 parameters) and the
blockiness of the sequence(the single remaining parameter).
In case of *M* = 2, telegraph matrix can be made from those parameters
as follows.
| |
(1) |

where blockiness,
the probability of state *j*.
The blockiness is obtained from the exponential coefficient
of well logs' correlation data. The left term of the right hand side
describes the tendency to remain in the same state as before, and
the right one is for the tendency to change into another state.
Markov chains depend only on the last state. Once the current state
is determined, it forgets all the previous states and choose the
next state only from the current information.
If the first state is state 1, the probability state
vector . The probability for the continuous state
becomes
| |
(2) |

After obtaining , a random number (from 0 to 1)
is used to choose new
state and we get the new for the next lottery.

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Stanford Exploration Project

11/17/1997